Question

Two integers have a product of −24 and a sum of −10. What are the values of the two integers?

_________________ and _________________

Answer 1

`xy=-24\\ x+y=-10\\\\ xy=-24\\ x=-10-y\\\\ (-10-y)y=-24\\ -10y-y^2+24=0\\ y^2+10y-24=0\\ y^2+12y-2y-24=0\\ y(y+12)-2(y+12)=0\\ (y-2)(y+2)=0\\ y=2 \vee y=-12\\\\ x=-10-2 \vee x=-10-(-12)\\ x=-12 \vee x=2`

So, these numbers are -12 and 2.